global system_name_sim i_ppp_sim x_0_sim y_sim u_sim A_u_sim simpar_sim

  ## Defaults
  if nargin<7
    extras.alpha = 0.1;
    extras.criterion = 1e-5;
    extras.emulate_timing = 0;

    extras.max_iterations = 10;
    extras.simulate = 1;
    extras.v = 1e-5;
    extras.verbose = 0;
  endif

  ##Estimate if we have some adjustable parameters
  estimating_parameters = (length(i_par)>0)
  
  ## Names
  s_system_name = sprintf("s%s", system_name);

  ## System details -- defines simulation within ol interval
  par = eval(sprintf("%s_numpar;", system_name));
  simpar = eval(sprintf("%s_simpar;", system_name));

  x_0_model = x_0;
  [n_x,n_y,n_u] = eval(sprintf("%s_def;", system_name));

  ## Sensitivity system details -- defines moving horizon simulation
  simpars = eval(sprintf("%s_simpar;", s_system_name));
  pars = eval(sprintf("%s_numpar;", s_system_name));
  x_0s = eval(sprintf("%s_state(pars);", s_system_name));
  x_0_models = x_0s;

  ## Times
  ## -- within opt horizon
  n_Tau = round(simpars.last/simpars.dt);
  dtau = simpars.dt;
  Tau = [0:n_Tau-1]'*dtau;
  [n_tau,n_w] = size(w_s);

      T_ol = n_ol*dt;		# Length of ol interval
      t_open = [t_open;T_ol];

      ## Generate input to actual system
      u_star_t = ppp_ustar(A_u,1,t_ol',0,0,n_u-n_U);

      ## Tune parameters/states
      if (estimating_parameters==1)
	## Save up the estimated parameters
	par_est = pars(i_par(:,1))
	p = [p; par_est'];

	## Set up according to interval length
	if (T_ol>T_ol_0) ## Truncate data
	  simpar_est.last = T_ol_0;
	  y_est = y_ol(1:n_t+1,:);
	else
	  simpar_est.last = T_ol;
	  y_est = y_ol;
	endif

	simpar_pred.last = T_ol_0; # Predicted length of next interval
	pars(i_ppp(:,1)) = U_old; # Update the simulation ppp weights
	
	## Optimise
	tick = time;
	[pars,Par,Error,Y,its] = \
	    ppp_optimise(s_system_name,x_0_models,pars,simpar_est,u_star_t,y_est,i_par,extras);
II = [1:length(y_est)]; plot(II,y_est,"*", II,Y)
	est_time = time-tick;  
	t_est = [t_est;est_time];
	its_est = [its_est; its-1];
      endif

      ## Update internal model
      par(i_ppp(:,3)) = U_old; # Update the internal model ppp weights

      if (estimating_parameters==1)
	par(i_par(:,3)) = pars(i_par(:,1)); # Update the internal model params
      endif

      simpar_model.last = T_ol;
      [y_model,x_model] = eval(sprintf("%s_sim(x_0_model, par, simpar_model, \
 					       u_star_t);",system_name));

      x_0 = x_model(n_ol+1,:)';	# Initial state of next interval
      x_0_model = x_0;
      x_0_models(1:2:(2*n_x)-1) = x_0_model;

      ## Compute U by optimisation
      tick = time;

      ## Predict state at start of next interval
      par(i_ppp(:,3)) = U;
      [y_next,x_next] = eval(sprintf("%s_sim(x_0, par, simpar, \
					     u_star_t);",system_name));
      x_next = x_next(n_t+1,:)'; # Initial state for next time
      x_nexts(1:2:(2*n_x)-1) = x_next; # And for internal sensitivity model
      
      ## Optimize for next interval      
      U_old = U;		# Save previous value
      U = expm(A_u*T_ol)*U;	# Initialise from continuation trajectory
      pars(i_ppp(:,1)) = U;	# Put initial value of U into the parameter vector
      [U, U_all, Error, Y, its] = ppp_nlin(system_name,x_nexts,pars,simpars,u_star_tau,w_s,i_ppp,extras);